# Another Special Right Triangle (Guided Discovery)

Interact with the applet below for a few minutes. After doing so, please answer the questions that appear below. You can move points A and B around at any time.

## 1.

How would you classify by its sides? Why would you classify it this way?

## 2.

What is the measure of the dark purple angle? Explain why your answer is true.

## 3.

What is the measure of ? Explain how you know this is true.

## 4.

What is the measure of angle A? Explain how you know.

## 5.

What are the measures of the interior angles of ?

## 6.

How does the length of the longest side of compare to the length of its shortest side? Explain how you know this to be true.

## 7.

Suppose AO = 3. What is the value of AC?

## 8.

Given that AO = 3 and your response to (7) above, solve for the length CO. Write your answer in simplest radical form.

## 9.

Answer questions (7) - (8) again, this time with AO = 4.

## 10.

Answer questions (7) - (8) again, this time with AO = 5.

## 11.

Answer questions (7) - (8) again, this time with AO = 6.

## 12.

Answer questions (7) - (8) again, this time with AO = 7.

## 13.

Notice any patterns in your data above? If so, explain the relationships you've discovered as best as you can.

## 14.

Answer questions (7) - (8) again, this time with AO = x. (Be sure your responses to these questions are expressions written in terms of x.)